Transfer operators for coupled analytic maps

We consider analytically coupled circle maps (uniformly expanding and analy tic) on the Z(d)-lattice with exponentially decaying interaction. We introd uce Banach spaces for the infinite-dimensional system that include measures whose finite-dimensional marginals have analytic, exponentially bounded de nsities. Using residue calculus and 'cluster expansion'-like techniques we define transfer operators on these Banach spaces. We get a unique (in the c onsidered Banach spaces) probability measure that exhibits exponential deca y of correlations.